Dispersion properties of electrostatic sound wave modes in carbon nanotubes

The theoretical analysis of electrostatic sound wave modes in multiwalled carbon nanotubes is presented within the framework of the fluid theory in conjunction with the Poisson's equation. The electron and ion components of each wall of nanotubes are regarded as two-species plasma system, in which the perturbed electron number density is deduced by means of the quantum hydrodynamic model, while the ion density perturbation follows the classical expression. An analytical expression of the dispersion relation is obtained for the quantum ion-acoustic wave oscillations in the system. Numerical result is prepared for a two-walled carbon nanotube, giving rise to a splitting of the frequencies of the electrostatic oscillations due to the small coupling between the two cylinders.